Fill space between inner mesh
I went with the delete all but the outermost option (well, I kept two layers of the four you had). You have a circular opening in the top of the inside of the helmet. Select all the faces of its rim. I used circle (C) select for this and panned around until all were selected.
  

Delete these faces (X then F)
  

Select one face on the unwanted geometry
  

Select linked (CtrlL)
  

Delete everything that's selected (X then F)
  

It now looks like this (with all selected, zoomed out and limit selection to visible disabled)
  

I hope this helps.